Question

The sum of coefficients in the expansion of (1-2x+5x^2)^n is a and the sum of the coefficients in the expansion of (1-x)^2n is



b.Then

Answer 1

For sum of coefficients put x=1 in the expansion , put x=1 in the 1st and 2 expansion you will get a=b.

Answer 2

The required relation is a = b.

Step-by-step explanation:

1st expression = (1 - 2x + 5x²)ⁿ

Put x = 1. Then the sum of the coefficients of the expansion is given by

a = (1 - 2 + 5)ⁿ = 4ⁿ

2nd expression = (1 + x)²ⁿ

[ We take the 2nd expression to be (1 + x)²ⁿ, otherwise, when x = 1, the given expression vanishes. ]

Put x = 1. Then the sum of the coefficients of the expansion is given hy

b = (1 + 1)²ⁿ = 2²ⁿ

We see that, 4ⁿ = (2²)ⁿ = 2²ⁿ

i.e., a = b

This is the required relation.

Try it at home:

If the sum of the coefficients of the expansion of (1 - 3x + 10x²)ⁿ is p and that of (1 + x²)ⁿ is q, then find the relation between p and q.